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KVPY Sample Paper KVPY Stream-SX Model Paper-19

  • question_answer
    The value of \[\int\limits_{-2}^{2}{\frac{{{\sin }^{2}}x}{[x/\pi ]+1/2}dx,}\] where [  ] represent G.I.F -

    A) 1

    B) 0

    C) \[4-\sin 4\]

    D) None

    Correct Answer: B

    Solution :

    \[f(-x)=\frac{{{\sin }^{2}}x}{[-x/\pi ]+1/2}=\frac{{{\sin }^{2}}x}{-1-[x/\pi ]+1/2}\]
    \[f(-\,x)=\frac{{{\sin }^{2}}x}{1/2+[x/\pi ]}=-\,f(x)\]
    odd function \[\therefore \,\,Ans.=0\]


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